Derivation
Make a triangle with the sides a, b, and c, and angles A, B, and C. Draw the altitude from vertex C to the side across c; by definition it divides the original triangle into two right angle triangles. Mark the length of this line h.
It can be observed that:
Therefore
and
Doing the same thing with the line drawn between vertex A and side a will yield:
Read more about this topic: Law Of Sines